Table 2 (for time-overlapping scenario 2).

Comparison of the corrected Z-test and the naive t-test for two overlapping regions over partially overlapping intervals (Region 1: 1978–1993 vs. region 2: 1989–2004), in which case σ₁₂ = −141.25 < 0. APC1 and APC2 are the annual percent changes in Regions 1 and 2, respectively.

site	APC1	APC2	naive T-test	Corrected Z-test	estimated residual variance
All Malignant Cancers	−0.5	−0.5	0.075	0.052	6.81E-05
	−0.5	−0.3	0.840	0.830	6.84E-05
	−0.5	−0.1	1.00	0.99	6.82E-05
	−0.3	−0.3	0.075	0.058	6.77E-05
	−0.3	−0.1	0.843	0.831	6.78E-05
	−0.3	0.1	1.00	1.00	6.74E-05
	−0.1	−0.1	0.074	0.052	6.67E-05
	−0.1	0.1	0.851	0.831	6.65E-05
	−0.1	0.3	1.00	1.00	6.62E-05
	0.1	0.1	0.073	0.054	6.58E-05
	0.1	0.3	0.854	0.831	6.54E-05
	0.1	0.5	1.00	0.99	6.53E-05
	0.3	0.3	0.071	0.054	6.62E-05
	0.3	0.5	0.859	0.846	6.51E-05
	0.3	0.7	1.00	1.00	6.44E-05
	0.5	0.5	0.075	0.054	6.42E-05
	0.5	0.7	0.862	0.849	6.40E-05
	0.5	1.0	1.00	1.00	6.35E-05
Prostate Cancer	−0.5	−0.5	0.076	0.052	0.00061
	−0.5	−0.3	0.198	0.189	0.00061
	−0.5	−0.1	0.540	0.517	0.00061
	−0.5	0.1	0.850	0.837	0.00061
	−0.3	−0.3	0.075	0.050	0.00060
	−0.3	−0.1	0.199	0.183	0.00059
	−0.3	0.1	0.544	0.523	0.00058
	−0.3	0.3	0.854	0.840	0.00057
	−0.1	−0.1	0.075	0.058	0.00057
	−0.1	0.1	0.201	0.185	0.00057
	−0.1	0.3	0.545	0.526	0.00057
	−0.1	0.5	0.95	0.97	0.00057
	0.1	0.1	0.074	0.053	0.00057
	0.1	0.3	0.203	0.186	0.00057
	0.1	0.5	0.550	0.530	0.00057
	0.1	0.7	0.859	0.845	0.00057
	0.3	0.3	0.075	0.051	0.00057
	0.3	0.5	0.205	0.188	0.00057
	0.3	0.7	0.555	0.533	0.00057
	0.3	1.0	0.941	0.933	0.00057
	0.5	0.5	0.075	0.052	0.00056
	0.5	0.7	0.205	0.190	0.00056
	0.5	1.0	0.736	0.717	0.00056